Interacting hard-core bosons and surface preroughening

TL;DR

This paper develops a theoretical framework for the preroughening transition of surfaces using interacting step models mapped onto a bosonic quantum system, revealing conditions for the disordered flat phase.

Contribution

It introduces a novel mapping of surface step interactions onto a two-species bosonic model, incorporating finite terraces and revealing a rich phase diagram including the disordered flat phase.

Findings

Disordered flat phase stabilized by short-range repulsions.

On-site repulsion of up-down steps is crucial for phase stability.

Step-step correlations and terrace distributions can be computed directly.

Abstract

The theory of the preroughening transition of an unreconstructed surface, and the ensuing disordered flat (DOF) phase, is formulated in terms of interacting steps. Finite terraces play a crucial role in the formulation. We start by mapping the statistical mechanics of interacting (up and down) steps onto the quantum mechanics of two species of one-dimensional hard-core bosons. The effect of finite terraces translates into a number-non-conserving term in the boson Hamiltonian, which does not allow a description in terms of fermions, but leads to a two-chain spin problem. The Heisenberg spin-1 chain is recovered as a special limiting case. The global phase diagram is rich. We find the DOF phase is stabilized by short-range repulsions of like steps. On-site repulsion of up-down steps is essential in producing a DOF phase, whereas an off-site attraction between them is favorable but not required. Step-step correlation functions and terrace width distributions can be directly calculated with this method.